Toaster ovens have far less thermal mass to ride out power outages than full sized ovens, in addition to being less insulated as Jefromi said. They are going to be more sensitive to power outages. I think that skews you towards trying short duration items like cookies or mini-muffins, rather than larger items if the risk is high. You have to ask yourself what is the pattern, duration, frequency and likelihood of the outages and assess the risk before you start baking something.

Since this is not a conventional full-sized oven, should I invest in pizza stone for --ANY-- reason which can benefit my toaster oven assuming my aim is to bake breads and cookies?

I am not aware of a pizza stone manufactured to fit a small oven like this, but have read, in many places, that an unglazed ceramic tile is a good substitute for a pizza stone. I am not certain it would achieve your goal, but I can't believe that it would hurt.
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Cos CallisJan 21 '13 at 12:22

I cannot speak to availability in India, but at Amazon (US) carries at least one pizza stone sized for toaster ovens, and googling finds other results. I have no personal experience with this in toaster ovens, of course, but the reviews of the item on Amazon are quite mixed: evidently a lot of people receive it broken during shipping, but if it arrives intact, they tend to like it. See amazon.com/Kitchen-Supply-Toaster-7-inch-10-inch/dp/B000QJBNHY/…
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SAJ14SAJJan 21 '13 at 12:34

@AnishaKaul, I can't say specifically, but suspect that the open ended question in the title is what drew the 'downvote'. Such questions tend to be hard for others to evaluate objectively, but I thought your question (with a specific goal) was a good.
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Cos CallisJan 21 '13 at 12:41

@CosCallis I have not edited the question in the "text" to make it generic. :) You said: open ended question in the title is what drew the 'downvote'. Lately I have witnessed a lot unexplained downvotes on many of my questions - Perhaps someone is stalking me! :)
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abcdJan 21 '13 at 12:46

@AnishaKaul Unexplained downvotes happen to all of us, I think. You learn to just ignore them. Some people just like doing that.
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SAJ14SAJJan 21 '13 at 12:46

1 Answer
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In a small toaster oven, using a pizza stone is likely to be a tradeoff:

Toasting -- counter-productive, because it will shield the bottom of the bread (or other item) from the direct radiative heat from the bottom elements; you would want to remove the stone for this use.

Broiling (or as it is called in the British parlance if I understand correctly, grilling) -- Probably not a good idea. In a full sized oven, the stone would be left far enough from the heating elements that it would not be subject to intense radiative heat. In a toaster oven, it might be too close to the elements when the oven is used this way, so might be subject to cracking due to a higher temperature gradient and uneven thermal expansion.

General baking -- will require a longer a pre-heating period for the oven/stone to come up to temperature, but once at temperature, will provide a buffering effect for more even heating.

Convenience -- in full sized ovens, people often leave the stone in all of the time, and cook on a different rack if they don't want direct contact with the stone. This may or may not be possible or convenient in a toaster oven, so you may be constantly removing or putting back the stone based on your current use

Note that all of the above is just reasoning based on known facts; I haven't tried a pizza stone in a toaster oven, and wouldn't do so, as they have a generally low thermal mass. I tend to think of them as tools for toasting and reheating, not for primary cooking, baking, or roasting.